Answer:
A pencil costs $0.50
A binder costs $3.00
A notebook costs $2.50
Step-by-step explanation:
Represent Notebook with N, Pencil with P and Binder with B
For Anna:.
2N + P + 3B = 14.50
For Josh:.
N + 4P + B = 7.50
For Alex:
3N + 2P + 2B = 14.50
Required
Solve for N, P and B
Make N the subject in the second equation
N + 4P + B = 7.50
N = 7.50 - 4P - B
Substitute 7.50 - 4P - B for N in the first equation
2N + P + 3B = 14.50
2(7.50 - 4P - B) + P + 3B = 14.50
Open Bracket
15.0 - 8P - 2B + P + 3B = 14.50
Collect like terms
3B - 2B + P - 8P = 14.50 - 15.0
B - 7P = -0.50
B = 7P - 0.50
Substitute 7.50 - 4P - B for N in the third equation
3N + 2P + 2B = 14.50
3(7.50 - 4P - B) + 2P + 2B = 14.50
22.50 - 12P - 3B + 2P + 2B = 14.50
Collect Like Terms
2P -12P + 2B - 3B = 14.50 - 22.50
-10P - B = -8
Multiply through by -1
10P + B = 8
Recall that B = 7P - 0.50
10P + B = 8 becomes
10P + 7P - 0.50 = 8
17P - 0.50 = 8
17P = 8 + 0.50
17P = 8.50
Divide through by 17
P = 8.50/17
P = 0.50
This implies that a pencil costs $0.50
Substitute 0.50 for P in B = 7P - 0.50
B = 7 * 0.50 - 0.50
B = 3.50 - 0.50
B = 3.00
This implies that a binder costs $3.00
Substitute 3.00 for B and 0.50 for P in N = 7.50 - 4P - B
N = 7.50 - 4 * 0.50 - 3.00
N = 7.50 - 2.00 - 3.00
B = 2.50
This implies that a notebook costs $2.50
